13/10x-3=4/5x+15

Solution for 13/10x-3=4/5x+15 equation:

13/10x-3=4/5x+15

We move all terms to the left:

13/10x-3-(4/5x+15)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x+15)!=0

x∈R


We get rid of parentheses

13/10x-4/5x-15-3=0

We calculate fractions


65x/50x^2+(-40x)/50x^2-15-3=0

We add all the numbers together, and all the variables

65x/50x^2+(-40x)/50x^2-18=0

We multiply all the terms by the denominator


65x+(-40x)-18*50x^2=0

Wy multiply elements

-900x^2+65x+(-40x)=0

We get rid of parentheses

-900x^2+65x-40x=0

We add all the numbers together, and all the variables

-900x^2+25x=0

a = -900; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-900)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-900}=\frac{-50}{-1800}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-900}=\frac{0}{-1800}
=0
$